This is a phase I study of paclitaxel as a radiation sensitizer in the treatment of unresectable mesothelioma and non-small cell lung cancer. The purpose is to determine the maximum tolerated dose of paclitaxel when delivered as a 20-hour continuous infusion every 3 weeks concurrently with thoracic irradiation to include the primary tumor site and appropriate draining lymph nodes for non-small cell lung cancer patients. Hemithorax irradiation will be employed for patients with mesothelioma. Another goal of this protocol is to understand the biology of lung cancer and mesothelioma as well as to assess the effectiveness of paclitaxel against these tumors. To achieve this goal, we will examine, among other studies, the labeling index of tumor specimens with the use of the in vivo iododeoxyuridine (IUdR) labeling technique. Studies of in vivo IUdR labeling at other centers include breast, lung, prostate, gastric, and colon carcinomas. There are very limited data from IUdR labeling of mesothelioma. We have accrued 30 patients on the protocol. The maximum tolerated dose has been determined to be 105mg/m2 infused over five days. The dose limiting toxicity at 120mg/m2 was hematologic (neutropenia) and GI (nausea and vomiting). Local control was 77% with predominant mode of failure distant metastases. One of five patients biopsied was found to have a small G2/M block characteristic of paclitaxel.